Numerical algorithm and complexity analysis for diagonalization of multivariate homogeneous polynomials
Rings and Algebras
2025-03-04 v2 Number Theory
Abstract
We study the computational complexity of a diagonalization technique for multivariate homogeneous polynomials, that is, expressing them as sums of powers of independent linear forms. It is based on Harrison's center theory and consists of a criterion and a diagonalization algorithm. Detailed formulations and computational complexity of each component of the technique are given. The complexity analysis focuses on the impacts of the number of variables and the degree of given polynomials. We show that this criterion runs in polynomial time and the diagonalization process performs efficiently in numerical experiments. Other diagonalization techniques are reviewed and compared in terms of complexity.
Cite
@article{arxiv.2310.14042,
title = {Numerical algorithm and complexity analysis for diagonalization of multivariate homogeneous polynomials},
author = {Lishan Fang and Hua-Lin Huang and Yuechen Li},
journal= {arXiv preprint arXiv:2310.14042},
year = {2025}
}